Proving Parallel Lines

Front

What are vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Front

What are alternate interior angles?

Back

Alternate interior angles are pairs of angles that lie on opposite sides of a transversal and inside the two lines. If the lines are parallel, these angles are equal.

Front

What are corresponding angles?

Back

Corresponding angles are pairs of angles that are in the same position on two different lines cut by a transversal. If the lines are parallel, these angles are equal.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they are in the same plane and do not intersect, no matter how far they are extended.

Front

What is the relationship between supplementary angles?

Back

Supplementary angles are two angles whose measures add up to 180 degrees.

Front

If ∠3 and ∠4 are supplementary, what can be concluded about the lines they are associated with?

Back

If ∠3 and ∠4 are supplementary and formed by a transversal intersecting two lines, then the lines are parallel.

Front

What condition proves that lines l and m are parallel using angle congruence?

Back

If ∠1 ≅ ∠3 or ∠3 ≅ ∠5, then lines l and m are parallel.

Front

How can you determine if two lines are parallel using angle measures?

Back

If the measures of alternate interior angles are equal or if corresponding angles are equal, the lines are parallel.

Front

What is the significance of angle pairs in proving parallel lines?

Back

Angle pairs such as alternate interior angles, corresponding angles, and supplementary angles are used to establish the parallelism of lines.

Front

What is the value of x that shows lines l and m are parallel if ∠5 = 2x + 4 and ∠6 = 3x - 8?

Back

Set 2x + 4 + 3x - 8 = 180 and solve for x. The value of x that shows lines l and m are parallel is 24.